459 research outputs found
Ramsey fringes formation during excitation of topological modes in a Bose-Einstein condensate
The Ramsey fringes formation during the excitation of topological coherent
modes of a Bose-Einstein condensate by an external modulating field is
considered. The Ramsey fringes appear when a series of pulses of the excitation
field is applied. In both Rabi and Ramsey interrogations, there is a shift of
the population maximum transfer due to the strong non-linearity present in the
system. It is found that the Ramsey pattern itself retains information about
the accumulated relative phase between both ground and excited coherent modes.Comment: Latex file, 12 pages, 5 figure
Graph hypersurfaces and a dichotomy in the Grothendieck ring
The subring of the Grothendieck ring of varieties generated by the graph
hypersurfaces of quantum field theory maps to the monoid ring of stable
birational equivalence classes of varieties. We show that the image of this map
is the copy of Z generated by the class of a point. Thus, the span of the graph
hypersurfaces in the Grothendieck ring is nearly killed by setting the
Lefschetz motive L to zero, while it is known that graph hypersurfaces generate
the Grothendieck ring over a localization of Z[L] in which L becomes
invertible. In particular, this shows that the graph hypersurfaces do not
generate the Grothendieck ring prior to localization. The same result yields
some information on the mixed Hodge structures of graph hypersurfaces, in the
form of a constraint on the terms in their Deligne-Hodge polynomials.Comment: 8 pages, LaTe
Regulating atomic imbalance in double-well lattices
An insulating optical lattice with double-well sites is considered. In the
case of the unity filling factor, an effective Hamiltonian in the pseudospin
representation is derived. A method is suggested for manipulating the
properties of the system by varying the shape of the double-well potential. In
particular, it is shown that the atomic imbalance can be varied at will and a
kind of the Morse-alphabet sequences can be created.Comment: Latex file, 12 pages, 3 figure
Hill's Equation with Random Forcing Parameters: Determination of Growth Rates through Random Matrices
This paper derives expressions for the growth rates for the random 2 x 2
matrices that result from solutions to the random Hill's equation. The
parameters that appear in Hill's equation include the forcing strength and
oscillation frequency. The development of the solutions to this periodic
differential equation can be described by a discrete map, where the matrix
elements are given by the principal solutions for each cycle. Variations in the
forcing strength and oscillation frequency lead to matrix elements that vary
from cycle to cycle. This paper presents an analysis of the growth rates
including cases where all of the cycles are highly unstable, where some cycles
are near the stability border, and where the map would be stable in the absence
of fluctuations. For all of these regimes, we provide expressions for the
growth rates of the matrices that describe the solutions.Comment: 22 pages, 3 figure
Moving constraints as stabilizing controls in classical mechanics
The paper analyzes a Lagrangian system which is controlled by directly
assigning some of the coordinates as functions of time, by means of
frictionless constraints. In a natural system of coordinates, the equations of
motions contain terms which are linear or quadratic w.r.t.time derivatives of
the control functions. After reviewing the basic equations, we explain the
significance of the quadratic terms, related to geodesics orthogonal to a given
foliation. We then study the problem of stabilization of the system to a given
point, by means of oscillating controls. This problem is first reduced to the
weak stability for a related convex-valued differential inclusion, then studied
by Lyapunov functions methods. In the last sections, we illustrate the results
by means of various mechanical examples.Comment: 52 pages, 4 figure
Defining < A^2 > in the finite volume hamiltonian formalism
It is shown how in principle for non-abelian gauge theories it is possible in
the finite volume hamiltonian framework to make sense of calculating the
expectation value of ||A||^2=\int d^3x(A^a_i(x))^2. Gauge invariance requires
one to replace ||A||^2 by its minimum over the gauge orbit, which makes it a
highly non-local quantity. We comment on the difficulty of finding a gauge
invariant expression for ||A||^2_{min} analogous to that found for the abelian
case, and the relation of this question to Gribov copies. We deal with these
issues by implementing the hamiltonian on the so-called fundamental domain,
with appropriate boundary conditions in field space, essential to correctly
represent the physics of the problem.Comment: 13 pages, 2 figures (in 3 parts). Amended references. Modified
introduction. Version accepted for publicatio
QED Effective Action at Finite Temperature: Two-Loop Dominance
We calculate the two-loop effective action of QED for arbitrary constant
electromagnetic fields at finite temperature T in the limit of T much smaller
than the electron mass. It is shown that in this regime the two-loop
contribution always exceeds the influence of the one-loop part due to the
thermal excitation of the internal photon. As an application, we study light
propagation and photon splitting in the presence of a magnetic background field
at low temperature. We furthermore discover a thermally induced contribution to
pair production in electric fields.Comment: 34 pages, 4 figures, LaTe
Discrete Nonholonomic Lagrangian Systems on Lie Groupoids
This paper studies the construction of geometric integrators for nonholonomic
systems. We derive the nonholonomic discrete Euler-Lagrange equations in a
setting which permits to deduce geometric integrators for continuous
nonholonomic systems (reduced or not). The formalism is given in terms of Lie
groupoids, specifying a discrete Lagrangian and a constraint submanifold on it.
Additionally, it is necessary to fix a vector subbundle of the Lie algebroid
associated to the Lie groupoid. We also discuss the existence of nonholonomic
evolution operators in terms of the discrete nonholonomic Legendre
transformations and in terms of adequate decompositions of the prolongation of
the Lie groupoid. The characterization of the reversibility of the evolution
operator and the discrete nonholonomic momentum equation are also considered.
Finally, we illustrate with several classical examples the wide range of
application of the theory (the discrete nonholonomic constrained particle, the
Suslov system, the Chaplygin sleigh, the Veselova system, the rolling ball on a
rotating table and the two wheeled planar mobile robot).Comment: 45 page
Power Corrections and KLN Cancellations
We consider perturbative expansions in theories with an infrared cutoff
. The infrared sensitive pieces are defined as terms nonanalytic in
the infinitesimal and powers of this cutoff characterize the
strength of these infrared contributions. It is argued that the sum over the
initial and final degenerate ( as ) states which is required by
the Kinoshita - Lee - Nauenberg theorem eliminates terms of order
and . However, the quadratic and higher order terms in general do
not cancel. This is investigated in simple examples of KLN cancellations, of
relevance to the inclusive decay rate of a heavy particle, at the one loop
level.Comment: 20 pages, LaTe
-Strands
A -strand is a map for a Lie
group that follows from Hamilton's principle for a certain class of
-invariant Lagrangians. The SO(3)-strand is the -strand version of the
rigid body equation and it may be regarded physically as a continuous spin
chain. Here, -strand dynamics for ellipsoidal rotations is derived as
an Euler-Poincar\'e system for a certain class of variations and recast as a
Lie-Poisson system for coadjoint flow with the same Hamiltonian structure as
for a perfect complex fluid. For a special Hamiltonian, the -strand is
mapped into a completely integrable generalization of the classical chiral
model for the SO(3)-strand. Analogous results are obtained for the
-strand. The -strand is the -strand version of the
Bloch-Iserles ordinary differential equation, whose solutions exhibit dynamical
sorting. Numerical solutions show nonlinear interactions of coherent wave-like
solutions in both cases. -strand equations on the
diffeomorphism group are also introduced and shown
to admit solutions with singular support (e.g., peakons).Comment: 35 pages, 5 figures, 3rd version. To appear in J Nonlin Sc
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